Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+8y &= 9 \\ 2x+4y &= 7\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -2x+7$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{1}{2}x + \dfrac{7}{4}}$ Substitute this expression for $y$ in the first equation. $-x+8({-\dfrac{1}{2}x + \dfrac{7}{4}}) = 9$ $-x - 4x + 14 = 9$ Simplify by combining terms, then solve for $x$ $-5x + 14 = 9$ $-5x = -5$ $x = 1$ Substitute $1$ for $x$ back into the top equation. $- 1+8y = 9$ $-1+8y = 9$ $8y = 10$ $y = \dfrac{5}{4}$ The solution is $\enspace x = 1, \enspace y = \dfrac{5}{4}$.